A generalization of the fundamental theorem of de Finetti for imprecise conditional probability assessments

In this paper, based on a suitable generalization of the coherence principle of de Finetti, we consider imprecise probability assessments on finite families of conditional events and we study the problem of their extension. Then, we extend some theoretical results and an algorithm, previously obtained for precise assessments, to the case of imprecise assessments and we propose a generalized version of the fundamental theorem of de Finetti. Our algorithm can be also exploited to produce coherent lower and upper probabilities. Moreover, we compare our approach to similar ones, like probability logic. Finally, we apply our algorithm to some well known inference rules under taxonomical knowledge.